Critical dividing surface

Figure 5. Schematic representation of O + H2 and O + HO IDCI) collisions. The heavy line repesents a part of the critical dividing surface, lighter lines represent equipotential contours. Ellipsoidal approximations are used for both kind of surfaces as described in the text, v is the relative velocity of the collision partners, R is their center-of-mass separation vector, y is te Jacobi angle, n is the normal to the equipotential energy surfeces. The coordinate origin is at the center of mass of the molecule axis x coincides with its longitudinal axis. In the present model calculations, straight line trajectories up to the critical dividing surface are assumed...

At the present level of rigour, the potential energy surface (Surface I) may be characterized by a critical dividing surface of roughly elUpsoidal shape with axes a = 2.57A and b = 0.69a, and the equipotential surfaces near the barrier which may also be... 

Figure 1. Schematic presentation of a short segment of a trajectory passing through an element dS of the potential energy surface near the critical dividing surface element dC. Defined are the relevant components of the relative velocity v of the collision partners. R is the vector joining the centers of mass of the colliding species, n is the unit vector in the direction of the potential gradient at dS.

The simplest way of taking account of vibrational effects is to assume vibrational adiabaticity during the motion up to the critical dividing surface [27]. As mentioned already in the Introduction, much of the earlier work on vibrational adiabaticity was concerned with its relationship to transition-state theory, especially as applied to the prediction of thermal rate constants [24-26]. It is pointed out in [27] that the validity of the vibrationally adiabatic assumption is supported by the results of both quasiclassical and quantum scattering calculations. The effective thresholds indicated by the latter for the D + H2(v =1) and O + H2(v =1) reactions [37,38] are similar to those found from vibrationally adiabatic transition-state theory, which is a strong evidence for the correctness of the hypothesis of vibrational adiabaticity. Similar corroboration is provided by the combined transition-state and quasiclassical trajectory calculations [39-44]. For virtrrally all the A + BC systems studied [39-44], both collinearly and in three... 

In reactions with vibrationally excited reagents additional shape effects may thns arise for two reasons [22]. First, the energies and form of the critical dividing surface for each vibrationally adiabatic state of the system will be different. Second, the physical shape of the reagent molecule may also depend on its vibrational states. In case of A + BC(v =... 

In the kinematic mass model investigation of the strong j dependence of the reaction cross-section in the O + H2 reaction [61] the shape of the critical dividing surface in the region relevant for the reaction was approximated by an ellipsoid with the axes a =... 

Fortunately, if one s objective is to determine only rate constants, one can employ transition state theory (TST), which has been comprehensively reviewed by Fernandez-Ramos et a/. In TST, attention is focused on the flux of trajectories through a critical dividing surface (or strictly, critical dividing hypersurface), S, which divides the phase space associated with reactants from that associated with products. In most cases, the location of S can be defined by just the positional co-ordinates of the system that is, in our example involving just three atoms rc )- For reactions involving IV atoms and... 

The transition state serves as a dynamical bottleneck such that once trajectories reach this bottleneck they pass through it to products without any turning back so that there is no re-crossing of the critical dividing surface. 

Up to this point I have described the development of TST for a canonical assembly of molecules, that is, to the situation where the distribution of reactant molecules among states is defined by the Boltzmann laws and a single temperature. It has been implicitly assumed that the location of the transition state (or critical dividing surface) is independent of the energy of the reactants. However, the microcanonical version of TST, referred to as /iTST can provide estimates of the rate coefficients, k E), for reactants of defined energy, and by integrating these values of k E) over the thermal distribution of energies, provide an improved estimate of k T). 

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